Superman is one of DC's mightiest mortals - a hero who, at times, has become the literal living embodiment of heroism. Under the right circumstances, readers expect Superman to be capable of righting any wrong, facing any foe, and staying loyal to truth, justice, and the American way while he does it. But DC's Man of Steel isn't magic - he's an alien who's getting beefed up by our yellow sun - and that means he has physical limits which fans often don't consider.
One of these limits is the need for sleep. While sleep is vital for humans, Superman naturally stores energy as he goes about his day. Trap him in darkness and he begins to weaken and die, bathe him in sunlight and he gets stronger and stronger. If he's living off solar energy to that extent, why would Superman need any shut-eye? On the other hand, Kryptonians didn't evolve with a yellow sun, so it's reasonable to assume he's from a culture and species who naturally require sleep to function. So, what's the answer? Does Superman sleep, does he dream, and does he need sleep to live?
The first of these questions is the easiest to answer: Superman can sleep. In JLA #22 by Grant Morrison, John Dell, and Howard Porter, Superman is affected by a "sleeping plague," demonstrating that he has the physical capacity to fall asleep, even when he's at full power. Of course, it's directed by an outside force, so we need a little more evidence. In Sandman #71, we get it, when Superman, Batman, and the Martian Manhunter are pictured as guests at the wake for Dream of the Endless - an event attended by every being capable of dreaming. Superman discusses dreams he's had in the past with Batman, humorously referencing out-of-canon stories and their respective TV shows. An interesting tidbit from this scene is that Superman's dreaming self is pictured as Clark Kent, while Batman remains in his costume, his face hidden by shadow, perhaps suggesting the identities these characters subconsciously accept as their true selves.
If Superman's self-reported dreams are accurate, he has them frequently enough to consider some of them recurring. From this, we can take it that Superman sleeps pretty frequently, but the question of why still remains. Kryptonians may have evolved to need sleep, but Superman is being supercharged by Earth's yellow sun, so what does he actually gain from sleeping and - if nothing - what governs when he sleeps, wakes, and dreams?
In 2020's Superman #9, Clark Kent zones out during a family discussion and then, by way of apology, shares Batman's theory on the matter:
I forgot to [sleep]. If I lived on Krypton I would sleep whatever a normal Kryptonian cycle was... but the yellow sun that gives us our powers here, makes it so I don't have to sleep, even though clearly I do. Batman said it was my subconscious screaming for its "stage time."
This raises a fascinating situation where Superman doesn't have to sleep for physical sustenance, but rather as a process for clearing his mind and allowing him to focus. This is ed by Superman's words in 1981's Superman #365, where he thinks:
Whew! The past five days were supposed to be a vacation for Clark Kent, but ever since I took off my glasses, I've been confronted by a never-ending stream of crises and catastrophes! It's been one monumental job for Superman after another! There's nothing I'd like better than to be sacked-out in my apartment or my Arctic Fortress of Solitude right now, but I promised Kara I'd stop by New York for our regular weekly rendezvous. True, she and I don't need anywhere near as much sleep as Earth people do, but after five sleepless days and nights, even a Kryptonian can start to go a little bonkers.
The issue continues with Superman coming into conflict with Supergirl, who is experiencing symptoms which he identifies as similar to sleep deprivation (though they're caused by an outside force.)
Here, then, we have our answer - Superman is kept physically rejuvenated by a supply of yellow sunlight, but he needs to sleep a small amount every five days or less to organize his thoughts and stay mentally healthy. While this may sound minor, Supergirl is driven to dangerous mania by her sleep deprivation, attempting to kill Superman despite their close relationship. In this sense, Superman may be able to physically survive by replacing sleep with sunlight, but unless he gets at least a little sleep once a week, all those around him are in danger. Because of this, the answer to the question of whether Superman needs to sleep is yes, but it's for the health of those around him rather than his own.